Voltage current sensor with high matching directivity

ABSTRACT

A technique for measuring the current, voltage and phase of an RF power wave to an RF load, accounts for the finite length of the voltage and current pickups, and corrects for effects of standing wave components of voltage and current. Voltage and current are computed as complex functions of the voltage pickup signal and the current pickup signal, based on coefficients precalibrated for said-predetermined radio frequency. Alternatively, a corrected current value can based on the corrected voltage value and complex load impedance. The correction coefficients can be obtained, for each of a plurality of calibrating radio frequencies within an RF range, from voltage and current pickup signals under conditions of (a) open circuit load, (b) short circuit load, (c) fixed known impedance load; and (d) one of voltage and current being applied at a precise input level to a known load from an RF calibration source. The voltage and current probe can comprise a metal housing having a cylindrical bore therethrough, and first and second recesses, a center conductor and cylindrical insulator within said bore and voltage and current sensor boards mounted in the recesses.

BACKGROUND OF THE INVENTION

[0001] This invention relates to accurate measurement of voltage,current and phase of RF power applied to a non-linear load, and isparticularly directed to probes for detecting the current, voltage, andphase of radio frequency (RF) electrical power that is being supplied toan RF plasma chamber.

[0002] In a typical RF plasma generator arrangement, a high power RFsource produces an RF wave at a preset frequency, i.e., 13.56 MHz, andthis is furnished along a power conduit to a plasma chamber. Becausethere is typically a severe impedance mismatch between the RF powersource and the plasma chamber, an impedance matching network isinterposed between the two. There are non-linearities in the plasmachamber, and because of these and because of losses in the line and inthe impedance matching network, not all of the output power of the RFgenerator reaches the plasma chamber. Therefore, it is conventional toemploy a probe in close proximity to the power input to the plasmachamber to detect the voltage and current of the RF wave as it entersthe plasma chamber. By accurately measuring the voltage and current asclose to the chamber as possible, the user of the plasma process canobtain a better indication of the quality of the plasma. This in turnyields better control of the etching or deposition characteristics for asilicon wafer or other workpiece in the chamber.

[0003] At present, diode detection probes are often employed to detectthe amplitude of the current and voltage waveforms. These probes simplyemploy diode detector circuits to rectify the voltage and currentwaveforms, and deliver simple DC metering outputs for voltage and forcurrent. These probes have at least two drawbacks in this role. Diodedetectors are inherently non-linear for low-signal levels, and arenotorious for temperature drift. The diode detector circuits also arelimited to detecting the signal peaks for the fundamental frequencyonly, and cannot yield any information about higher or lower frequenciespresent in the RF power waveform. In addition to this, it is impossibleto obtain phase angle information between the current and voltagewaveforms, which renders the power measurement less accurate.

[0004] One proposal that has been considered to improve the detection ofRF power has been to obtain digital samples of the voltage and currentoutputs of a probe, using flash conversion, and then to process thesamples on a high-speed buffer RAM. However, this proposal does haveproblems with accuracy and precision. At the present time, flashconversion has a low dynamic range, normally being limited to eight bitsof resolution. To gain reasonable phase accuracy for plasma customerrequirements, it is necessary to reach a precision of at least twelvebits, so that a phase angle precision of better than one degree can beobtained at full power. In addition, flash converters require anextremely fast RAM in order to buffer a block of samples before they areprocessed in a digital signal processor (DSP), and fast RAM circuitry isboth space-consuming and expensive.

[0005] Voltage and current probes that are now in existence are limitedin their performance by the fact that they can only monitor the voltage,current, and phase angle at one frequency, and even then such probeshave a poor dynamic range. Examining behavior at a different frequencyrequires changing out the hardware, which can be costly and timeconsuming. This means also that good performance will ensue only if theload is linear, which is never the case with a plasma chamber. Unlikecapacitors, inductors, and resistors, plasma chambers impose a highlynon-linear load, which causes the sinusoidal waveform of the input powerto become distorted. This distortion causes the resulting waveform to bea sum of sinusoids, with the frequency of each additional sinusoid beingsome integer multiple of the input sinusoidal frequency (i.e.,harmonics). Conventional probes can provide voltage, current and coarsephase information, at best, for the fundamental voltage and currentwaveforms. This severely limits the accuracy of the system, and makesaccurate and repeatable control impossible when there is a significantamount of voltage or current appearing in the harmonics.

[0006] A possible solution to this has been proposed in U.S. patentapplication Ser. No. 08/684,833, filed Jul. 22, 1996, and having thesame assignee as the present patent application. In that case, thevoltage/current probe employs a frequency shifting arrangement thatconverts the sampled voltage and current to a lower frequency basebandsignal to facilitate accurate detection of RF current and voltage of theapplied power, as well as phase information, with the baseband beingapproximately 0.2 KHz to 15 KHz. The baseband voltage and currentsignals are digitized and processed to obtain voltage and currentinformation, and using complex fast fourier transform technique, toobtain accurate phase information. That application Ser. No. 08/684,833is incorporated herein by reference.

[0007] Even with this technique, it remains to provide a super-highmatching directivity voltage and current sensor that behaves as if ithas a zero probe length, and which accurately reports the voltage,current, and phase conditions at the RF load. The problem in doing thisarises because any real voltage probe and any real current probe willhave a finite length, and the current and voltage waveforms are not flatover the length of the sensor.

[0008] A voltage-current probe, or V/I probe, is a sensor that isintended to produce output signals that represent a zero-length point atwhich it is inserted. On the other hand, any realistic sensor must be ofa finite size to sense the voltage or current. The V/I probe produces alow-level signal which has a well-defined relationship with respect tothe high-level signal (i.e., applied current or applied voltage) that isbeing measured. The fact that the probe or sensor has finite length,coupled with the fact that the applied power and the real-worldnon-ideal load produce standing waves, means that the RF voltage (orcurrent) is not going to be identical everywhere along its finitelength. It is also the case that the effect of non-uniformity over thelength of the sensor increases at higher frequencies, e.g., harmonics ofthe applied RF power. Unfortunately, nothing in the current state of theart compensates for this, and a calibration algorithm for the V/I probeis heretofore unknown in the art.

OBJECTS AND SUMMARY OF THE INVENTION

[0009] It is an objective of this invention to provide a reliable andaccurate probe, at low cost, for detecting the current and voltage of RFpower being applied to a plasma chamber and for accurately finding theload impedance (which may have real and imaginary components) as well asphase angle between the voltage and current applied to the load.

[0010] It is a more specific object of this invention to provide animproved voltage and current pickup head that accurately measures the RFvoltage and current at the point of injection of an RF power wave intoan RF load.

[0011] It is a further object to provide a V/I probe with a calibrationalgorithm to compensate for the non-zero length of the voltage andcurrent sensors of the probe.

[0012] According to an aspect of the invention, RF voltage and currentlevels and relative phase information for current and voltage can bederived for an RF power wave that is applied at a predetermined RFfrequency to a load, such as the power input of a plasma chamber. TheV/I probe produces a voltage pickup value V_(V) and a current pickupvalue V_(I). However, because the sensors for voltage and current are offinite length, and are not simply points, the technique of thisinvention compensates to produce corrected values of voltage, current,as well as impedance and phase. This involves computing the voltage as acomplex function of the voltage pickup signal and the current pickupsignal, based on coefficients precalibrated for the particular operatingradio frequency, and also computing the current as a complex function ofthe voltage and current pickup signals based on coefficientspre-calibrated for that operating radio frequency. This can also becarried out by computing a corrected voltage value as a complex functionof the voltage pickup signal and the current pickup signal, based oncoefficients precalibrated for the operating radio frequency, computinga complex impedance of the load at the operating radio frequency on thebasis of the voltage and current pickup signals, and then computing acorrected current value based on the corrected voltage value and thecomplex impedance. By “complex impedance” it should be understood thatthe load impedance may have both a “real” or resistive component and an“imaginary” or reactive (either capacitive or inductive) component.

[0013] The signal processor is calibrated with correction factors foreach of a number of frequencies within a range. These values areacquired by obtaining voltage and current pickup signals, for each of anumber of calibrating radio frequencies within the range, underconditions of (a) open circuit load, (b) short circuit load, (c) fixedknown impedance load, e.g., fifty ohms, and (d) either a knowncalibration voltage or a known current being applied at a precise inputlevel to a known load from an RF calibration source. Then the digitalsignal processor computes and stores the correction coefficients basedon the voltage and current signal values obtained under these conditions(a) to (d). These coefficients are obtained for each of the calibrationfrequencies in the overall range of interest. When the system isoperated at a particular selected operating frequency, the storedcorrection coefficients are applied to the voltage and current pickupsignals to obtain corrected voltage, corrected current, and a correctedload impedance value.

[0014] Computing the amplitudes and relative phase of the voltage andcurrent signals is carried out in the digital signal processor. For anyoperating frequency between successive calibrating radio frequencies forwhich the correction coefficients are stored, correction coefficientsare applied by interpolating between stored values for each suchcorrection coefficient for the calibration frequencies above and belowthe selected operating frequency.

[0015] The voltage and current probe has a metal housing having acylindrical bore therethrough, and first and second recesses, therecesses each opening to said bore for an axial distance. Voltage andcurrent sensor boards fit into these recesses, as discussed shortly.There is a center conductor extending along the axis of the bore and acylindrical insulator within the bore. The insulator surrounds thecenter conductor and extends radially between the conductor and thehousing. A voltage sensor board is mounted in the first recess and has acapacitive pickup plate facing radially towards the axis of the bore.The current sensor board is mounted in the second recess and has anelongated inductive pickup conductor, e.g., a wire, positioned to faceradially towards the the of the bore and extending axially for thepredetermined distance mentioned earlier. In a preferred embodiment, thefirst and second recesses are positioned opposite one another on themetal housing across the axis of the bore.

[0016] In many possible embodiments the voltage sensor board and currentsensor board each can include, in order radially outward, the capacitiveplate or pickup wire, an insulator layer, a ground plate completionconductive layer, and a circuit board carrying voltage pickupcomponents, with at least one electrical conductor passing from thecapacitive plate or inductive wire through openings in the insulatorlayer and the ground plate completion conductive layer to saidrespective voltage or current pickup components.

[0017] In similar fashion, the current sensor board can be formed, inorder radially outward, of the inductive pickup conductor, an insulatorlayer, a ground plate completion conductive layer, and a circuit boardcarrying current pickup components. At least one electrical conductorpasses from each end of the inductive pickup conductor through openingsin the insulator layer and ground plate completion conductive layer tothe current pickup components. Preferably the voltage and current pickupcomponents are symmetrically distributed upon the respective boards,both geometrically and electrically.

[0018] The above and many other embodiments of this invention willbecome apparent from the ensuing detailed description of a preferredexample, which is to be read in conjunction with the accompanyingDrawing.

BRIEF DESCRIPTION OF THE DRAWING

[0019]FIG. 1 is a block diagram of an RF plasma chamber, with associatedRF plasma generator, impedance match network, V-I sensor, and V-Ianalysis circuitry, according to an embodiment of this invention.

[0020]FIGS. 2A and 2B are end and side sectional views illustrating thetransmission line structure of the sensor of this invention.

[0021]FIG. 3 is an exploded sectional view of the sensor of anembodiment of the invention.

[0022]FIG. 4 is a sectional view of the voltage sensor board of thisembodiment.

[0023]FIGS. 4A to 4D are plan views showing respective layers of thevoltage sensor board.

[0024]FIG. 5 is a sectional view of the current sensor board of thisembodiment.

[0025]FIGS. 5A to 5D are plan views showing respective layers of thecurrent sensor board.

[0026]FIG. 6 is a schematic diagram for explaining transmission linecharacteristics of this invention.

[0027]FIG. 7 is a simplified schematic for explaining the voltage sensorof this embodiment.

[0028]FIG. 8 is a redrawn schematic for explaining the voltage sensor.

[0029]FIG. 9 is a simplified schematic for explaining the current sensorof this embodiment.

[0030]FIG. 10 is a redrawn schematic for explaining the current sensor.

[0031]FIG. 11 is a simplified diagram is a simplified diagram showingequivalence of mutual inductance to T-inductance.

[0032]FIG. 12 is an equivalent circuit diagram corresponding to that ofFIG. 10.

[0033]FIG. 13 is a circuit diagram explaining equivalence according toThevenin's Theorem.

[0034]FIG. 14 is an illustration of a working circuit for explainingThevenin conversion.

[0035]FIG. 15 is a Thevenin-equivalent circuit corresponding to FIG. 12.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0036] With reference to the Drawing, and initially to FIG. 1, a plasmaprocess arrangement 10, e.g., for etching a silicon wafer or otherworkpiece, has an RF power generator 12, which produces RF power at aprescribed frequency, e.g., 13.56 MHz at a predetermined power level,such as one kilowatt. The generator 12 supplies RF power along a conduit14 to a matching network 16. The output of the matching network 16 iscoupled by a power conduit 18 to an input of a plasma chamber 20. Aprobe voltage and current pickup device 22 picks up a voltage sampleV_(V) that represents the RF voltage V_(RF) and also picks up a currentsample voltage V_(I) that represents the RF current I_(RF) of theapplied RF power as it enters the input to the chamber 20. The chamber20 has a vacuum conduit associated with a not-shown vacuum pump and agas inlet through which a noble gas, e.g., argon, is introduced into thechamber. The voltage and current samples V_(V) and V_(I) are fed to avoltage and current (V-I) baseband probe arrangement 24 which measuresthe magnitudes or amplitudes of the applied voltage and current, andalso computes the phase angle Φ between the applied voltage and currentwaveforms. These three values can be computed with high accuracy, andcan in turn be used to calculate other parameters. In this arrangement,there is a digital controller that is programmable, e.g., by means of anexternal computer 28 configured with a modular P.D.S. encoding system.The controller 26 can be configured to control the RF generator 12, thephase and magnitude factors for the impedance match net 16, and otheradditional elements, such as a pressure controller 30 for the gaspressure supplied to the chamber 20. There can be additional sensorsconnected between the controller 26 and elements such as the chamber 20and the RF generator 12. This configuration is discussed at length incopending U.S. patent application Ser. No. 08/______, filed Oct. ______,1997, by Daniel F. Vona, et al. (Attorney Docket No. 675.032PA) having acommon assignee herewith.

[0037] The baseband V-I probe permits accurate determination of voltageamplitude |V|, current amplitude |I|, and phase Φ between voltage andcurrent for an RF (radio frequency) signal. This can be in the range of0.200 MHz to 67.8 MHz, permitting the user to analyze a plasma withgreater precision than has been possible with more conventional analogtechniques. The same concept can be applied beyond these frequencies toother ranges. End results of this improved capability include improvedprocess repeatability, improved process endpoint determination, higheryields, and more consistent yields. The V-I probe, when employed inconnection with the RF path in an RF plasma system, allows the user toachieve a higher degree of control, and to achieve control usingparameters beyond simply peak voltage and current values of the RF wave.With the baseband V-I probe arrangement the user can control the plasmaprocess based on power delivered to the plasma, whether at the RFfrequency of the generator or at any other frequency, impedance of theplasma, either at the frequency of the RF waveform or at any frequencywithin the bandwidth of the arrangement. For example, harmonic analysiscan be used for a more accurately determination of completion for anetching step in an integrated circuit (IC) wafer.

[0038] It should be appreciated that with this probe arrangement, theabove parameters are obtained with an improvement in smaller size, lowercost, lower drift, higher accuracy (especially at high phase angles) andwith greater flexibility of integration than with existing probe systemsor techniques. Moreover, unlike conventional, diode based systems, thearrangement of permits harmonic analysis and permits plasma power andimpedance measurements at user-selected frequencies. Also, this probearrangement permits the data to be easily exported, and facilitatesremote user operation and monitoring.

[0039] The phase measurement taken in this manner is highly accurate,i.e., to within one-fifth degree, i.e., 0.2°. This cannot be achievedwith other techniques, such as zero-crossing detectors.

[0040] Of course, this probe can be used over a wide range offrequencies, including other process RF frequencies such as 27.12 MHz,40.68 MHz, etc.

[0041] A problem of achieving precision in measuring the voltage,current, and phase arises from the fact that the voltage and currentsensors have to be of finite size in order to pick up a detectablesignal. Therefore, this invention addresses the problem of creating asuper-high matching directivity voltage and current sensor and allowingfor the calibration of the non-zero length of each. An ideal voltage andcurrent sensor should produce pickup signals Vv and Vi that represent azero-length insertion point. This is unrealistic, however, because thesensor has to be of finite size in order to sense the voltage andcurrent. The voltage and current sensor produces a low-level signalwhich has a well-defined relationship between itself and the high levelsignal being detected and measured. Accordingly, the achievement of thisinvention is to create a voltage and current sensor with super-highmatching directivity, and to generate a calibration algorithm to accountfor, and compensate for the non-zero length of the sensor elements.

[0042] Details of the hardware for the sensor 22 can be appreciated fromFIGS. 2A and 2B, which represent the V/I sensor 22 as a length ofcoaxial cable. The sensor 22 is created to behave as a length of coaxialtransmission line, with a center conductor A, a cylindrical insulatorlayer B of dielectric material such as air, Teflon, ceramics, or othersuitable material, and an outer conductor C that is coaxial with thecenter conductor A and the insulator B. The remaining structure of thesensor as shown in FIGS. 3, 4, 5, 4A to 4D, and 5A to 5D, serves todetect the voltage V_(RF) appearing on the center conductor A and thecurrent I_(RF) that flows through it. As shown in FIG. 3, the outerconductor C is formed as a generally rectangular aluminum housing 30,with an axial bore 32 in which the insulator B and center conductor Aare positioned. The housing 30 also has a recess 34 on one side (here,the top) in which a voltage sense circuit board is fitted, and anotherrecess 36 opposite the first recess in which a current sense circuitboard is fitted. Various plates and attachments fit on this, but are notshown here. The recesses 34 and 36 extend radially inward and meet with,that is, open onto, the center bore 32. This structure maintains theelectrical characteristics of a coaxial line, but allows for theelectric signals to be sensed.

[0043] The housing 30 here has a square outside and a cylindrical hole32 on the inside. Due to the fact that the RF current does notcompletely penetrate an electrical conductor, i.e., due to “skineffect,” the current travels through the housing near the central bore32, and not through the square portion beyond it. Consequently, themeasurement of the RF current and voltage requires introducing thecurrent and voltage measurement elements into the structure shown inFIG. 2 at or close to the cylindrical surface defined by the bore 32.

[0044] The printed circuit board 20 has a capacitive plate 52 formedthereon, as shown in section in FIG. 4, shown also in FIG. 4A. Theconductive plate has a length L and is positioned facing the centerconductor A and parallel with it. This is placed on an insulator layer43 (FIG. 4B) on which is mounted a ground completion conductive layer 44(FIG. 4C), which also has a portion surrounding the margin of theinsulator layer 43. A printed circuit board 45 is positioned on the sideradially away from the capacitive plate 42 (FIG. 4D). There arefeed-throughs 46 and 47 disposed at transverse positions on the plate 42and on a line midway beween its ends. The feed-throughs pass through thelayers 43, 44, and 45 to connect to circuit elements 48 on the PCB 45.As shown here, the elements 48 should be distributed symmetrically onthe board, both axially and transversely.

[0045] The printed circuit board 50 with an inductive wire 52 formed(i.e., printed) thereon is shown in section in FIG. 5, shown also inFIG. 5A. The inductive wire has a length L and is positioned facing thecenter conductor A and parallel with it. This wire 52 is placed on aninsulator layer 53 (FIG. 5B) on which is mounted a ground completionconductive layer 54 (FIG. 5C), which also has a portion surrounding themargin of the insulator layer 53. A printed circuit board 55 ispositioned on the side radially away from the inductive wire 52 (FIG.5D). There are feed-throughs 56 and 57 disposed at the ends of theinductive wire 52 and passing through the layers 53, 54, and 55 toconnect to circuit elements 58 on the PCB 55. As shown here, theelements 58 should be distributed symmetrically on the board, bothaxially and transversely. Also, the voltage and current sensor elementsshould be the same length.

[0046] In this embodiment, the voltage and current sensing elements areplaced on opposite sides of the center conductor in order to minimizecrosstalk between the two circuit boards 40 and 50. In each case theground completion layer 44, 54 serves as the ground plane layer C forthe outer conductor, and also completes the return path for current inthe main coaxial line section with minimal disruption.

[0047] Theory of Operation of Voltage and Current Sense Printed CircuitBoards:

[0048] Due to the laws of AC field and wave electromagnetics, thevoltage present on the center conductor of the coaxial transmission line(FIG. 2) induces a voltage in the metallic plate 42, (similar inoperation to a capacitor). These same laws of electromagnetics cause thecurrent traveling through the center conductor of the coaxialtransmission line to induce a current in the metallic wire 52 (similarin operation to a transformer). The design of the coaxial line section(including printed circuit board lengths) is constrained by the factorsof: (a) breakdown voltage; (b) current carrying capacity; (c)characteristic impedance; and (d) voltage and current pickupsensitivity.

[0049] Breakdown voltage is determined by the distance between thecenter and outer conductors and the breakdown voltage of the insulatingmaterial between them. The greater the distance, the larger thebreakdown voltage. Current carrying capacity is determined by the sizeof each of the two conductors; with the size of the inner conductorbeing the main factor because of its smaller diameter. The larger thediameter, the larger the current carrying capacity. Characteristicimpedance is determined by the diameters of the inner and outerconductors and the dielectric constant of the insulating materialbetween them. Finally, pickup sensitivity is determined by the length ofeach pickup and the distance between each pickup and the innerconductor. The net effect is that increasing the length of thecapacitive plate 42, or the metallic wire 52 or moving either closer tothe center conductor of the coaxial transmission line will increase theamount of voltage or current, respectively, that is induced in each. Aproper balance between all four of these factors is necessary foroptimal operation of the V/I sensor.

[0050] Symmetry of each PCB 40, 50 about the center conductor of thecoaxial line section (in both the long and short directions) is the keyto achieving identical sensitivity to the forward and reverse travelingvoltage and current waves present in the coaxial line section. Identicalsensitivity produces a balanced system with a balanced ground system.This sensitivity is referred to as “matching directivity”. Accuracy ofthe sensor over wide impedance ranges demands an almost perfectsensitivity (or a super high matching directivity.)

[0051] Examination of Linearity:

[0052] With the coaxial voltage sensing structure outlined above,additional design goals where placed upon the circuit which would bepresent on the outer layer 45 or 55 (circuit construction) for eachsensing PCB. One of these design goals is to produce a voltage signalthat was a linear representation (in both phase and magnitude) of thevoltage on the main line section. The second design goal is to produce avoltage signal that is a linear representation (in both phase andmagnitude) of the current signal on the main line section. With theseconstraints satisfied, the magnitudes of the voltage and current signalas well as the phase angle between these signals can easily becalculated according to the equations below:

V _(D) =V _(VI) *V _(G)  (1)

I _(D) =V _(II) *I _(G)  (2)

Φ=ΦV _(VI) −ΦV _(II)  (3)

[0053] Where:

[0054] V_(D): Voltage Displayed

[0055] V_(VI): Voltage at Voltage Input

[0056] V_(G): Voltage Gain Coefficient

[0057] I_(D): Current Displayed

[0058] V_(II): Voltage at Current Input

[0059] I_(G): Current Gain Coefficient

[0060] Φ: Phase Angle Between Voltage and Current

[0061] ΦV_(VI):Phase of Voltage at Voltage Input

[0062] ΦV_(II): Phase of Voltage at Current Input

[0063] Laboratory experimentation reveals that the original designobjective of linear in phase and magnitude is not possible withconventional circuitry. The equations presented in (1), (2), and (3)above caused significant computational errors when the V/I Probe wasconnected to low and high impedance loads; with the error increasingwith frequency.

[0064] Calibration Algorithm Description:

[0065] Another aspect of this invention involves an analysis of theequations in (1), (2), and ( 3) to demonstrate that they not valid.Next, the invention involves finding the equations that actuallydescribe sensor behavior. Finally, the invention involves how toproperly calibrate for the hardware described hereinabove in such a wayas to allow the new equations to be valid over a maximum frequency rangeand impedance range.

[0066] Since the V/I sensor was created as a coaxial line segment, thebest place to start is to take a look at transmission line theory.Transmission line theory states that the voltage and current valuesproduced at different positions on a transmission line are a function ofthis position. This is shown graphically in FIG. 6, in which V_(G) andZ_(G) are applied RF voltage and impedance of the RF generator,respectively.

[0067] Equations (4) and (5) below define the rules that govern thetransmission line system shown in FIGS. 2A and 2B.

V(x)=I _(L)(Z _(L)*Cos h(γ*x)+Z ₀*Sin h(γ*x))  (4)

I(x)=(I _(L) /Z ₀)*(Z _(L)*Sin h(γ*x)+Z ₀*Cos h(γ*x))  (5)

[0068] Where:

[0069] V(x): Voltage as a function of position on the line

[0070] I(x): Current as a function of position on the line

[0071] x: Position on the line away from Z_(L) (with Z_(L) being x=0)

[0072] I_(L): Current at the load (at x=0)

[0073] Z_(L): Load impedance (at x=0)

[0074] V_(L): Voltage at load (at x=0)

[0075] Z₀: Characteristic impedance of transmission line

[0076] γ: Propagation constant of transmission line

[0077] In a lossless transmission line, the two constants Z₀ and γ aredefined as:

Z ₀={square root}(L/C)  (6)

γ=j*ω*{square root}(L*C)  (7)

[0078] Where:

[0079] L: Inductance of transmission line

[0080] C: Capacitance of transmission line

[0081] ω: Frequency of interest (radians per second)

[0082] Examination of Voltage Sensor:

[0083] Equation (4) clearly shows that the voltage produced on atransmission line as a function of position is only constant for thesituation when Z_(L)=Z₀. For all other values of Z_(L), the voltage mustbe computed with equation (4).

[0084] As stated previously, the voltage sensor is created by placingthe metal capacitive plate 42 of length L a fixed distance from thecenter conductor of a coaxial transmission line. This geometry creates acapacitance between the center conductor and the metal plate, allowingfor a small portion of the energy in the line to be tapped. It is thiscapacitance and the additional frequency shaping circuitry thatfunctions as a voltage sensor. FIG. 7 shows a rough sketch of thevoltage sensor, where:

[0085] L: Length of parallel voltage sensor plate along transmissionline center conductor

[0086] VP: Voltage at center of pickup (capacitive plate 42)

[0087] C_(L): Load capacitance for frequency smoothing of magnituderesponse

[0088] R_(L): Load resistance for frequency smoothing of magnituderesponse.

[0089] In practice, the above electromagnetic geometry is constructedinto a printed circuit board allowing easy construction, maintenance,repeatability, and reliability.

[0090] When a load is attached to a transmission line, the forward andreverse traveling AC waves combine to create a standing wave patternoriginating from the load. If the impedance of load exactly matches thecharacteristic impedance of the transmission line, the standing wavepattern is constant in magnitude for the entire length of thetransmission line. Since a perfect match between the impedance of theload and the impedance of the line is possible only in theory, astanding wave will always exist and the voltage will not be a constantvalue across the length of the metal plate of the voltage sensor. Hence,equation (4) must be utilized to properly calculate the voltage at pointV_(P). The challenge is to create an equation that can be calculated ina digital signal processor (DSP), micro-processor, etc. to produce anaccurate result. To solve this, we graphically combine equation (4) withFIG. 7 to produce the circuit shown in FIG. 8. Here, as series of ncapacitor elements represent the capacitance formed between the metalplate 42 on the voltage pickup and the inner conductor A of thetransmission line. In this case,

[0091] X: Position on voltage sensor plate for equation (4)

[0092] L: Length of voltage sensor plate parallel to the transmissionline conductor A

[0093] n: Number of equal length pieces length L is divided into

[0094] V₁, V₂, . . . V_(n): Voltages calculated from equation (4) at ndifferent values of X

[0095] I₁, I₂, . . . I_(n): Currents produced due to voltages V₁, V₂, .. . V_(n)

[0096] ΔC: Partial capacitance of voltage sensor created by capacitancedivided into n parts

[0097] I_(P): Sum of currents I₁, I₂, . . . I_(n); total current leavingpoint V_(P)

[0098] V_(P): Voltage at center of pickup plate 42

[0099] C_(L): Load capacitance for frequency smoothing of magnituderesponse

[0100] R_(L): Load resistance for frequency smoothing of magnituderesponse

[0101] Proper circuit analysis of FIG. 8 involves implementation ofKirchoff's current law (KCL). Doing this we get: $\begin{matrix}{I_{P} = {\sum\limits_{k = 1}^{n}I_{k}}} & (8)\end{matrix}$

[0102] Additionally, FIG. 8 shows the following relationships:

I _(P) =V _(P) /Z _(P)

=V _(P)/(Z _(CL) ∥R)  (9)

ΔC=C/n  (10)

ΔZ _(C)=1/(j*ω*ΔC)  (11)

I _(k)=(V _(n) −V _(p))/(ΔZ _(C))  (12)

ΔX=L/n  (13)

[0103] Where C is the capacitance formed by voltage sensor parallelplate 42. Combining equations (10) and (13) yields:

ΔC=C*(ΔX)/L  (14)

[0104] Combining equations (14) and (11) yields: $\begin{matrix}\begin{matrix}{{\Delta \quad Z_{C}} = {1/\left( {j*\omega*C*\Delta \quad {X/L}} \right)}} \\{= {L/\left( {j*\omega*C*\Delta \quad X} \right)}}\end{matrix} & (15)\end{matrix}$

[0105] Combining equations (15) and (12) yields: $\begin{matrix}\begin{matrix}{I_{k} = {{\left( {V_{n} - V_{P}} \right)/L}/\left( {j*\omega*C*\Delta \quad X} \right)}} \\{= {j*\omega*C*\left( {V_{n} - V_{P}} \right)*\Delta \quad {X/L}}}\end{matrix} & (16)\end{matrix}$

[0106] The summation notation in equation (8) is an approximation only,and hence, not exact. An exact solution requires increasing n to ∞,which is easily done with an integral. Rewriting equation (8) inintegral notation yields: $\begin{matrix}{I_{P} = {{\int_{0}^{L}{1\quad }}}} & (17)\end{matrix}$

[0107] Where dl is formed from I_(k):

d _(l) =j*ω*C*(V(X)−V _(P))*dX/L  (18)

[0108] Substituting equation (18) into (17) and working with the resultyields: $\begin{matrix}\begin{matrix}{I_{P} = \quad {\int_{0}^{L}{\frac{j \cdot \omega \cdot C \cdot \left( {{V(X)} - V_{P}} \right)}{L}\quad {X}}}} \\{= \quad {\frac{j \cdot \omega \cdot C}{L} \cdot {\int_{0}^{L}{\left( {{V(X)} - V_{P}} \right)\quad {X}}}}} \\{\frac{I_{P}}{j \cdot \omega \cdot C} = \quad {\frac{1}{L} \cdot {\int_{0}^{L}{\left( {{V(X)} - V_{P}} \right)\quad {X}}}}} \\{\quad {\frac{1}{L} \cdot \left( {{\int_{0}^{L}{{V(X)}\quad {X}}} - {V_{P} \cdot L}} \right)}} \\{\frac{I_{P}}{j \cdot \omega \cdot C} = \quad {{- V_{P}} + {\frac{1}{L} \cdot {\int_{0}^{L}{{V(X)}\quad {X}}}}}}\end{matrix} & (19)\end{matrix}$

[0109] Combining equations (19), (9), and (4) yields: $\begin{matrix}\begin{matrix}{\frac{V_{P}}{\left( Z_{P} \right) \cdot \left( {j \cdot \omega \cdot C} \right)} = \quad {{- V_{P}} + {\frac{1}{L} \cdot}}} \\{\quad {\int_{0}^{L}\left\lbrack {I_{L} \cdot \left( {{{Z_{L} \cdot \cosh}\quad \left( {\gamma \cdot X} \right)} + {Z_{0} \cdot}} \right.} \right.}} \\{\left. \quad {\sinh \left( {\gamma \cdot X} \right)} \right\rbrack \quad {X}}\end{matrix} & (20)\end{matrix}$

[0110] Solving equation (20) for V_(P) (the voltage at the pickup plate42) yields: $\begin{matrix}\begin{matrix}{{V_{P} \cdot \left\lbrack {1 + \frac{1}{\left( Z_{P} \right) \cdot \left( {j \cdot \omega \cdot C} \right)}} \right\rbrack} = \quad {\frac{1}{L} \cdot {\int_{0}^{L}\left\lbrack {I_{L} \cdot \left( {{{Z_{L} \cdot \cosh}\quad \left( {\gamma \cdot X} \right)} +} \right.} \right.}}} \\{{\quad \left. {Z_{0} \cdot {\sinh \left( {\gamma \cdot X} \right)}} \right\rbrack}\quad {X}} \\{= \quad {\left\lbrack {\frac{1}{L} \cdot {\int_{0}^{L}{\left\lbrack {I_{L} \cdot \left( {{Z_{L} \cdot \cosh}\quad \left( {\gamma \cdot X} \right)} \right)} \right\rbrack \quad {X}}}} \right\rbrack +}} \\{\quad \left\lbrack {\frac{1}{L} \cdot {\int_{0}^{L}{{I_{L} \cdot \left\lbrack {Z_{0} \cdot \left( {\sinh \quad \left( {\gamma \cdot X} \right)} \right)} \right\rbrack}\quad {X}}}} \right\rbrack} \\{= \quad {\left( {\frac{I_{L} \cdot Z_{L}}{L} \cdot {\int_{0}^{L}{\cosh \quad \left( {\gamma \cdot X} \right)\quad {X}}}} \right) +}} \\{\quad \left( {\frac{I_{L} \cdot Z_{0}}{L} \cdot {\int_{0}^{L}{\sinh \quad \left( {\gamma \cdot X} \right)\quad {X}}}} \right)} \\{= \quad {{\frac{I_{L} \cdot Z_{L}}{L \cdot \gamma} \cdot \left( {\sinh \left( {\gamma \cdot X} \right)} \right)_{0\ldots \quad L}} +}} \\{\quad {\frac{I_{L} \cdot Z_{0}}{L \cdot \gamma} \cdot \left( {\cosh \left( {\gamma \cdot X} \right)} \right)_{0\ldots \quad L}}} \\{= \quad {{\frac{I_{L} \cdot Z_{L}}{L \cdot \gamma} \cdot {\sinh \left( {\gamma \cdot L} \right)}} +}} \\{\quad {\frac{I_{L} \cdot Z_{0}}{L \cdot \gamma} \cdot \left( {{\cosh \left( {\gamma \cdot L} \right)} - 1} \right)}} \\{= \quad {{I_{L} \cdot Z_{L} \cdot \frac{\sinh \left( {\gamma \cdot L} \right)}{L \cdot \gamma}} + {I_{L} \cdot Z_{0} \cdot}}} \\{\quad \left( \frac{{\cosh \left( {\gamma \cdot L} \right)} - 1}{L \cdot \gamma} \right)}\end{matrix} & (21)\end{matrix}$

[0111] Since L is a constant always and γ is a constant at a givenfrequency (the V/I Probe is calibrated at separate frequencies), we canre-write the above as:${V_{P} \cdot \left\lbrack {1 + \frac{1}{\left( Z_{P} \right) \cdot \left( {j \cdot \omega \cdot C} \right)}} \right\rbrack} = {{I_{L} \cdot Z_{L} \cdot A} + {I_{L} \cdot Z_{0} \cdot B}}$

[0112] Also, since Z_(P) and j*ω*C will be constant at a givenfrequency, the above equation can be written as: $\begin{matrix}\begin{matrix}{{V_{P} \cdot D} = {{I_{L} \cdot Z_{L} \cdot A} + {I_{L} \cdot Z_{0} \cdot B}}} \\{V_{P} = \frac{{I_{L} \cdot Z_{L} \cdot A} + {I_{L} \cdot Z_{0} \cdot B}}{D}} \\\text{Where:} \\{A = {{{{Sinh}\left( {\gamma*L} \right)}/\left( {\gamma*L} \right)}\quad \text{(Constant~~for~~a~~single~~frequency)}}} \\{B = {{\left( {{{Cosh}\left( {\gamma*L} \right)} - 1} \right)/\left( {\gamma*L} \right)}\quad \text{(Constant~~for~~a~~single~~frequency)}}} \\{D = {1 + {{1/\left( {Z_{P}*j*\omega*C} \right)}\quad \text{(Constant~~for~~a~~single~~frequency)}}}}\end{matrix} & (22)\end{matrix}$

[0113] The expression in equation (22) has three constants. Thisequation is very important to the second part of this invention and willbe simplified later.

[0114] Examination of Current Sensor:

[0115] Equation (5) clearly shows that the current produced on atransmission line, as a function of position, is only constant for thesituation when Z_(L)=Z₀. For all other values of Z_(L), the current canbe calculated with equation (5).

[0116] As stated previously, the current sensor is created by placing aconductive wire of length L a fixed distance from the center conductor Aof a coaxial transmission line. This geometry creates a mutualinductance between the center conductor and the wire, and allows for asmall portion of the energy in the line to be tapped. It is this mutualinductance and the additional frequency shaping circuitry that functionsas a current sensor. FIG. 9 below shows a rough schematic of the currentsensor. Here,

[0117] L is the length of the parallel current sensor wire 52 along thetransmission line conductor,

[0118] Z_(I) is the current circuit load impedance, and

[0119] V_(I) is the voltage across the circuit load.

[0120] In practice, the above electromagnetic geometry is constructedinto a printed circuit board for easy construction, maintenance,repeatability, and reliability.

[0121] When a load is attached to a transmission line, the forward andreverse traveling waves combine to create a standing wave patternoriginating from the load. If the impedance of load exactly matches thecharacteristic impedance of the transmission line, the standing wavepattern is constant in magnitude for the entire length of thetransmission line. Since a perfect match between the impedance of theload and the impedance of the line is possible only in theory, astanding wave will always exist and the current will not be a constantvalue across the length of the metal wire of the current sensor. Hence,equation (5) must be utilized to properly calculate the voltage acrossimpedance Z_(I) produced by the current I_(I). The challenge, again, isto create an equation that can be calculated in a DSP, microprocessor,etc. to produce an accurate result. To solve this, we graphicallycombine equation (5) and FIG. 9 to produce FIG. 10, where thetransformer pairs represent the mutual inductance between the innerconductor of the transmission line and the current pickup wire of thecurrent sensor geometry, where: X: Position on current sensor wire forequation (5) L: Length of current sensor wire parallel to thetransmission line conductor A n: Number of equal length pieces length Lis divided into I₁, I₂, . . . I_(n): Currents calculated from equation(5) at n different values of X Z₁: Load impedance for frequencysmoothing of magnitude response V₁: Voltage produced across load Z₁ dueto currents I₁, I₂, . . . I_(n) ΔM: Partial mutual inductance created bymutual inductance/n ΔL₁: Partial primary transformer inductance createdby primary inductance, divided into n parts ΔL₂: Partial secondarytransformer inductance created by secondary inductance, divided into nparts.

[0122] The next step is to conduct circuit analysis on the circuit inFIG. 10. When analyzing a circuit with mutual inductance elements, it isusually most efficient to replace each mutual inductor with its “T”inductor equivalent circuit. This conversion is shown pictorially inFIG. 11.

[0123]FIG. 12 is a simplified version of FIG. 10, but is still toocomplicated for easy circuit analysis. Hence, the next step is tosimplify FIG. 12. The best place to start the simplification is toreplace each portion of the circuit (e.g., with the dashed box aroundit) with its Thevenin equivalent circuit. A Thevenin circuit utilizesthe Thevenin theorem (which states that any excited, fixed circuitnetwork can be replaced with an equivalent ideal voltage source andseries impedance) to complete the transformation. The Thevenin theoremis shown pictorially in FIG. 13. The circuit for Thevenin conversion isshown in FIG. 14. The Thevenin impedance (Z_(TH)) is found by replacingthe current source with an open circuit (representation of infiniteimpedance) and calculate the remaining impedance seen when “looking”between the terminals marked A and B: $\begin{matrix}\begin{matrix}{Z_{TH} = {j\quad \omega*\left( {{\Delta \quad L_{2}} - {\Delta \quad M} + {\Delta \quad M}} \right)}} \\{= {j\quad \omega*\Delta \quad L_{2}}}\end{matrix} & (23)\end{matrix}$

[0124] The Thevenin voltage is found by computing V_(AB) with an opencircuit between the terminals marked A and B:

V_(AB)=V_(TH)

V _(TH) =I _(n)*(jωΔM)  (24)

[0125]FIG. 15 represents the circuit of FIG. 12, simplified with theThevenin equivalent circuits in place, where

[0126] V_(TH1): Equivalent Thevenin voltage from sub circuit containingI₁

[0127] Z_(TH1): Equivalent Thevenin impedance from sub circuitcontaining I₁

[0128] V_(TH2): Equivalent Thevenin voltage from sub circuit containingI₂

[0129] Z_(TH2): Equivalent Thevenin impedance from sub circuitcontaining I₂

[0130] V_(THn): Equivalent Thevenin voltage from sub circuit containingI_(n)

[0131] Z_(THn): Equivalent Thevenin impedance from sub circuitcontaining I_(n)

[0132] The voltage of interest in the complete circuit analysis isvoltage V_(I) formed across Impedance Z_(I) by current I_(I) (not shownin FIG. 15) Hence, it becomes necessary to solve for current I_(I). Thisis done by proper use of Kirchoff's Voltage Law (KVL):

V _(THn) −. . . −V _(TH2) −V _(TH1) +I _(I)*(Z _(THn) +. . . +Z _(TH2)+Z _(TH1))=0  (25)

[0133] Converting equation (25) to summation notation yields:$\begin{matrix}{{I_{I^{-}}\left( {{\sum\limits_{k = 1}^{n}Z_{THk}} + Z_{I}} \right)} = {\sum\limits_{k = 1}^{n}V_{THk}}} & (26)\end{matrix}$

[0134] Combining equations (23), (24), and (26) yields: $\begin{matrix}{{{I_{I^{-}}\left( {{\sum\limits_{k = 1}^{n}{{j \cdot \omega \cdot \Delta}\quad L_{2}}} + Z_{I}} \right)} = {\sum\limits_{k = 1}^{n}{{I_{k} \cdot j \cdot \omega \cdot \Delta}\quad M}}}{{I_{I^{-}}\left( {{j \cdot \omega \cdot L_{2}} + Z_{I}} \right)} = {\sum\limits_{k = 1}^{n}{{I_{k} \cdot j \cdot \omega \cdot \Delta}\quad M}}}} & (27)\end{matrix}$

[0135] Next, the mathematical definition of ΔM (partial mutualinductance) needs to be established:

ΔM=M/n  (28)

ΔX=L/n  (29)

[0136] Combining equations (28) and (29) yields:

ΔM=M*(ΔX)/L  (30)

ΔM=M*(ΔX)/L  (31)

[0137] Combining equations (30) and (27) yields: $\begin{matrix}{{I_{I^{-}}\left( {{j \cdot \omega \cdot L_{2}} + Z_{I}} \right)} = {\sum\limits_{k = 1}^{n}{I_{k} \cdot j \cdot \omega \cdot \frac{{M \cdot \Delta}\quad X}{L}}}} & (32)\end{matrix}$

[0138] The summation notation in equation (32) is an approximation only,and hence, not exact. An exact solution requires increasing n to ∞,which is easily done with an integral. Rewriting equation (32) inintegral notation yields: $\begin{matrix}{{I_{I^{-}}\left( {{j \cdot \omega \cdot L_{2}} + Z_{I}} \right)} = {\int_{0}^{L}{{{I(x)} \cdot \frac{j \cdot \omega \cdot M}{L}}\quad {x}}}} & (33)\end{matrix}$

[0139] Combining equations (33) and (5) yields: $\begin{matrix}{\begin{matrix}{{I_{I^{-}}\left( {{j \cdot \omega \cdot L_{2}} + Z_{I}} \right)} = \quad {\frac{j \cdot \omega \cdot M}{L} \cdot {\int_{0}^{L}\left\lbrack {\frac{I_{L}}{Z_{0}} \cdot \left( {{Z_{L} \cdot {{Sinh}\left( {\gamma \cdot x} \right)}} +} \right.} \right.}}} \\{\left. {\quad \left. {Z_{0} \cdot {{Cosh}\left( {\gamma \cdot x} \right)}} \right)} \right\rbrack \quad {x}}\end{matrix}\begin{matrix}{{I_{I^{-}}\left( {{j \cdot \omega \cdot L_{2}} + Z_{I}} \right)} = \quad {\frac{j \cdot \omega \cdot M}{L} \cdot \left\lbrack {{\frac{I_{L} \cdot Z_{L}}{Z_{0}} \cdot \left( \frac{{{Cosh}\left( {\gamma \cdot L} \right)} - 1}{\gamma} \right)} +} \right.}} \\{\quad \left. {I_{L} \cdot \frac{{Sinh}\left( {\gamma \cdot L} \right)}{\gamma}} \right\rbrack}\end{matrix}\begin{matrix}{{I_{I^{-}}\left( {{j \cdot \omega \cdot L_{2}} + Z_{I}} \right)} = \quad {j \cdot \omega \cdot M \cdot \left\lbrack {{\frac{I_{L} \cdot Z_{L}}{Z_{0}} \cdot \left( \frac{{{Cosh}\left( {\gamma \cdot L} \right)} - 1}{\gamma \cdot L} \right)} +} \right.}} \\{\quad \left. {I_{L} \cdot \frac{{Sihn}\left( {\gamma \cdot L} \right)}{\gamma \cdot L}} \right\rbrack}\end{matrix}{{I_{I^{-}}\left( {{j \cdot \omega \cdot L_{2}} + Z_{I}} \right)} = \quad {j \cdot \omega \cdot M \cdot \left( {{\frac{I_{L} \cdot Z_{L}}{Z_{0}} \cdot B} + {I_{L} \cdot A}} \right)}}{I_{I} = {\left( \frac{j \cdot \omega \cdot M}{{j \cdot \omega \cdot L_{2}} + Z_{I}} \right) \cdot \left( {{\frac{I_{L} \cdot Z_{L}}{Z_{0}} \cdot B} + {I_{L} \cdot A}} \right)}}{I_{I} = {\left( \frac{j \cdot \omega \cdot M}{{j \cdot \omega \cdot L_{2}} + Z_{I}} \right) \cdot \left( {{\frac{B}{Z_{0}} \cdot V_{L}} + {A \cdot I_{L}}} \right)}}} & (34)\end{matrix}$

[0140] Since the voltage across the current circuit load impedance Z_(I)is I_(I)*Z_(I), equation (34) can be simplified as: $\begin{matrix}\begin{matrix}{V_{I} = {E \cdot \left( {{\frac{B}{Z_{0}} \cdot V_{L}} + {A \cdot I_{L}}} \right)}} \\\text{Where:} \\{A = {{{{Sinh}\left( {\gamma*L} \right)}/\left( {\gamma*L} \right)}\quad \text{(Constant~~for~~a~~single~~frequency)}}} \\{B = {{\left( {{{Cosh}\left( {\gamma*L} \right)} - 1} \right)/\left( {\gamma*L} \right)}\quad \text{(Constant~~for~~a~~single~~frequency)}}} \\{E = {{\left( {j*\omega*M*Z_{I}} \right)/\left( {{j*\omega*L_{2}} + Z_{I}} \right)}\quad \text{(Constant~~for~~a~~single~~frequency)}}}\end{matrix} & (35)\end{matrix}$

[0141] This completes the derivation of the voltage and current pickupcircuits. In summary, the two equations the define the output of thevoltage (equation (22)) and current (equation (35)) circuits in the V/Isensor. These two equations are restated below for clarity beforecontinuing with derivations: $\begin{matrix}{V_{V} = \frac{{I_{L} \cdot Z_{L} \cdot A} + {I_{L} \cdot Z_{0} \cdot B}}{D}} & (22) \\{V_{I} = {E \cdot \left( {{\frac{B}{Z_{0}} \cdot V_{L}} + {A \cdot I_{L}}} \right)}} & (35)\end{matrix}$

[0142] These equations are a good first step, but the end goal of thisderivation is to create a set of equations to allow a computer (i.e.DSP) to compensate (calibrate) for the non-ideal effect of the pickuphead (as summarized in the above equations.) A cursory glance at theabove two equations will show that there are five constants (A, B, D, E,and Z₀). Five constants means that there are five unknowns in thecalibration. Five unknowns means that five different measurementstandards need to be maintained (either equipment or impedancestandards) for each frequency. Five points at each frequency are toomany. The purpose of the remainder of this derivation section will be toreduce the number of constants needed. Starting with this goal, theabove two equations can be rewritten as:

V _(V) =F*V _(L) +G*I _(L)  (36)

V _(I) =H*V _(L) +J*I _(L)  (37)

[0143] Where:

[0144] F=A/D

[0145] G=Z₀*B/D

[0146] H=E*B/Z₀

[0147] J=E*A

[0148] Equations (36) and (37) now contain only four constants each.Since V_(V) and V_(I) will be known voltages (i.e. voltages measured bythe analysis section), equations (36) and (37) need to be solved forV_(L) and I_(L) (the load voltage and current respectively). Treatingequations (36) and (37) as a system of equations and solving the systemyields:

V _(L)=(J*V _(V) −G*V _(I))/(F*J−G*H)  (38)

I _(L)=(F*V _(I) −H*V _(V))/(F*J−G*H)  (39)

[0149] With V_(L) and I_(L) solved for, Z_(L) can easily be calculatedby:

Z _(L) =V _(L) /I _(L)

=(J*V _(V) −G*V _(I))/(F*V_(I) −H*V _(V))  (40)

[0150] Equations (38), (39), and (40) represent how to calculate theload values, but four constants are still too many (four constants meansmaintaining four unknowns during calibration.) Continuing on, if weremember that:

Z _(V) =V _(V) /V _(I)  (41)

[0151] Combining equations (40) and (41) yields:

Z _(L)=(J*Z _(V) −G)/(F−H*Z _(V))  (42)

[0152] Equation (42) still has four unknowns, but it allows Z_(L) (loadimpedance) to be computed directly from Z_(V) (impedance measured byanalysis board.) Two of the four unknowns can be calculated from a shortcircuit and open circuit. These will work well because an open circuitand short circuit are easy to maintain. Working equation (42) with ashort circuit at the load (Z_(L)=0) yields:

0=(J*Z _(V) −G)/(F−H*Z _(V))

0=J*Z _(V) −G

J*Z _(V) =G

Z _(V) =G/J  (43)

[0153] If a constant Z_(VS) is created to mean the impedance “seen” bythe analysis section when Z_(L) is a short circuit, a new constant iscreated and equation (43) becomes:

Z _(VS) =G/J  (44)

[0154] Equation (44) is a very important result—this will be shownlater. Working with equation (42) with an open circuit at the load(Z_(L)=∞) yields:

∞=(J*Z _(V) −G)/(F−H*Z _(V))

0=(F−H*Z _(V))/(J*Z _(V) −G)

0=(F−H*Z _(V))

H*Z_(V) =F

Z _(V) =F/H  (45)

[0155] If a constant Z_(VO) is created to mean the impedance “seen” bythe analysis section then Z_(L) is an open circuit, a new constant iscreated and equation (45) becomes:

Z _(VO) =F/H  (46)

[0156] Again, equation (46) is an important result. Combining equations(42), (44), and (46) yields: $\begin{matrix}\begin{matrix}{Z_{L} = {\left( {{J*Z_{V}} - G} \right)/\left( {F - {H*Z_{V}}} \right)}} \\{= {\left( {Z_{V} - {G/J}} \right)/\left( {\left( {1/J} \right)*\left( {F - {H*Z_{V}}} \right)} \right.}} \\{= {\left( {J/H} \right)*{\left( {Z_{V} - {G/J}} \right)/\left( {{F/H} - Z_{V}} \right)}}} \\{Z_{L} = {\left( {J/H} \right)*{\left( {Z_{V} - Z_{VS}} \right)/\left( {Z_{VO} - Z_{V}} \right)}}}\end{matrix} & (47)\end{matrix}$

[0157] Another impedance standard that is easy to maintain is a stable50 ohm load. If a constant Z_(LX) is created to mean the impedance“seen” by the analysis section when Z_(L) is the stable 50 ohm load, anew constant is created and equation (47) becomes:

Z _(L) =Z _(LX)*(Z _(V) −Z _(VS))/(Z _(VO) −Z _(V))  (48)

[0158] Four calibration standards are still needed, but each is easilymaintainable. In summary, the four standards are:

[0159] (1) Short Circuit Load

[0160] (2) Open Circuit Load

[0161] (3) Stable 50 ohm Load

[0162] (4) Voltage or Current Standard

[0163] Items (1)-(3) from the list above were addressed earlier, item(4) will be addressed now. At the moment, accurate RF voltagemeasurement equipment is easier to obtain than accurate RF currentmeasurement equipment. With this in mind, the equations for calculatingV_(L) and I_(L) (the load voltage and current) are easily created byworking with equations (38) and (39) respectively: $\begin{matrix}\begin{matrix}{{V_{L}} = {{\left( {{J*V_{V}} - {G*V_{I}}} \right)/\left( {{F*J} - {G*H}} \right)}}} \\{= {{\left( {V_{V} - {\left( {G/J} \right)*V_{I}}} \right)/\left( {F - {\left( {G/J} \right)*H}} \right)}}} \\{= {{\left( {V_{V} - {Z_{VS}*V_{I}}} \right)/\left( {F - {Z_{VS}*H}} \right)}}} \\{{V_{L}} = {{V_{I}*{\left( {Z_{V} - Z_{VS}} \right)/V_{C}}}}}\end{matrix} & (49) \\{{I_{L}} = {{V_{L}}/{Z_{L}}}} & (50)\end{matrix}$

[0164] Where V_(C) is a voltage calibration coefficient created fromvoltage measurement standard.

[0165] This derivation can be understood by an explanation of thecalibration and measurement cycle that will be utilized by the analysissection:

[0166] (1) It is established that calibration will only be completed forspecified frequencies in the bandwidth of the V/I Probe (otherwise, aninfinitely long calibration table would result).

[0167] (2) It is established that the V/I Probe will be calibrated at acertain number of frequencies per decade. The remaining gaps in thespectrum can be filled by simple linear interpolation between adjacent,calibrated frequency points.

[0168] (3) The 50 Ω load standard is measured (both impedance and phase)at each of the frequencies established in step (2). This loadinformation is made available to the DSP in the analysis section.

[0169] (4) A short circuit is connected to the V/I Probe and sufficientpower is run though the V/I sensor into the short circuit to createsignals strong enough to be measured by the analysis section. The DSP inthe analysis section computes the value Z_(V) by dividing the voltagesignal V_(V) by the current signal V_(I). This Z_(V) value is thenstored as the Z_(VS) calibration constant for the frequency measured.This is repeated for all frequencies chosen in step (2).

[0170] (5) An open circuit is connected to the V/I Probe and sufficientpower is run through the V/I sensor into the open circuit to createsignals strong enough to be measured by the analysis section. The DSP inthe analysis section computes the value Z_(V). This Z_(V) value is thenstored as the Z_(VO) calibration constant for the frequency measured.This is repeated for all frequencies chosen in step (2).

[0171] (6) The 50 Ω load standard is connected to the V/I Probe andsufficient power is run through the V/I sensor into the 50 Ω load tocreate signals strong enough to be measured by the analysis section. TheDSP in the analysis section computes the value Z_(V). This Z_(V)valuewith the data taken in steps (3) to (5) is used to compute thecalibration constant Z_(LX) which is stored for the frequency measured.This is repeated for all frequencies chosen in step (2).

[0172] (7) A load of any impedance is connected to the V/I Probe for thevoltage measurement standard and sufficient power is run through the V/Isensor and voltage measurement standard to create signals strong enoughto be measured by each. The DSP in the analysis section computes thevalue Z_(V). This Z_(V) value in addition to the data from the voltagemeasurement standard is used to compute the calibration constant V_(C)which is stored for the frequency measured. This is repeated for allfrequencies chosen in step (2).

[0173] Now, when data are requested from the V/I Probe the DSP simplyneeds to calculate Z_(V), extract the stored calibration constantsZ_(VS), Z_(VO), Z_(LX), and V_(C) and use them to calculate Z_(L),V_(L), and I_(L) using equations (48), (49), and (50) respectively. Withthese three calculations complete, the DSP has all the necessary data(i.e. |V|, |I|, |Z|, and ∠Z) to compute all other items requested by theoperator.

[0174] One unique point about this calibration method is that itsaccuracy is based solely upon how accurately the stable 50 Ω load can bemeasured and how accurate is the voltage standard. To improve accuracyof the calibration all that needs to be done is a more accuratemeasurement of the 50 Ω load and a more accurate voltage standard.

[0175] While the invention has been described in detail with referenceto a preferred embodiment, the invention is certainly not limited onlyto that embodiment, but may be applied in a wide range of environments.Rather, many modifications and variations will present themselves topersons of skill in the art without departing from the scope and spiritof this invention, as defined in the appended claims.

I claim:
 1. A method of deriving current, voltage and phase informationfor current and voltage components of an RF power wave that is appliedat a predetermined radio frequency (RF) to an RF load, and in which avoltage/current probe having a voltage pickup of finite length and acurrent pickup of finite length applies a voltage pickup signal V_(v)and a current pickup signal V_(i) to a signal processor which processessaid voltage and current pickup signals to produce values of voltage,current and phase appearing at said load and corrected for effects ofstanding wave components of voltage and current, comprising: computingsaid voltage as a complex function of the voltage pickup signal and thecurrent pickup signal, based on coefficients precalibrated for saidpredetermined radio frequency, and computing said current as a complexfunction of the voltage and current pickup signals based on coefficientspre-calibrated for said radio frequency.
 2. A method of derivingcurrent, voltage and phase information for current and voltagecomponents of an RF power wave that is applied at a predetermined radiofrequency (RF) to an RF load, and in which a voltage/current probehaving a voltage pickup of finite length and a current pickup of finitelength applies a voltage pickup signal V_(v) and a current pickup signalV_(i) to a signal processor which processes said voltage and currentpickup signals to produce values of voltage, current and phase appearingat said load and corrected for effects of standing wave components ofvoltage and current, comprising: computing a corrected voltage value asa complex function of the voltage pickup signal and the current pickupsignal, based on coefficients precalibrated for said predetermined radiofrequency, computing a complex impedance of said load at saidpredetermined radio frequency on the basis of said voltage and currentpickup signals, and computing a corrected current value based on saidcorrected voltage value and said complex impedance.
 3. A method ofderiving current, voltage and phase information for current and voltagecomponents of an RF power wave, at a selected operating frequencyselected within a range of radio frequencies, which power wave isapplied to an RF load, and in which a voltage/current probe having avoltage pickup of a finite length and a current pickup of a finitelength applies a voltage pickup signal V_(v) and a current pickup signalV_(i) to a signal processor which processes said voltage and currentpickup signals to produce values of voltage, current, and phaseappearing at said load, and corrected for effects of standing wavecomponents of voltage and current; comprising, for each of a pluralityof calibrating radio frequencies within said range, obtaining voltageand current pickup signals under conditions of (a) open circuit load,(b) short circuit load, (c) fixed known impedance load; and (d) one ofvoltage and current being applied at a precise input level to a knownload from an RF calibration source; and computing and storing correctioncoefficients based on the voltage and current signal values obtainedunder said conditions (a) to (d); and at said selected operatingfrequency, applying stored correction coefficients to said voltage andcurrent pickup signals to obtain one or more of a corrected voltagevalue, a corrected current value, and a corrected load impedance value.4. The method of claim 3 wherein, for a selected operating frequencybetween successive calibrating radio frequencies for which saidcorrection coefficients are stored, said step of applying storedcorrection coefficients includes interpolating between stored values foreach said correction coefficient for the calibration frequencies aboveand below said selected operating frequency.
 5. The method of claim 3,wherein said fixed known impedance is a 50 ohm resistive load.
 6. Themethod of claim 3, wherein said radio frequencies are in the range ofabout 0.2 megahertz to about a hundred megahertz.
 7. Voltage and currentprobe for detecting voltage and current values of an RF power wave thatis applied therethrough to an RF load, comprising: a metal housinghaving a cylindrical bore therethrough, and first and second recesses,the recesses each opening to said bore for an axial distance; a centerconductor extending along the axis of said bore; a cylindrical insulatorwithin said bore surrounding said center conductor and extendingradially between said conductor and said housing; a voltage sensor boardmounted in the first recess and having a capacitive pickup plate facingradially towards the axis of the bore; and a current sensor boardmounted in the second recess and having an elongated inductive pickupconductor facing radially towards the axis of the bore and extendingaxially for said axial distance.
 8. The voltage and current sensor as inclaim 7, wherein said first and second recesses are positioned oppositeone another on said metal housing across the axis of said bore.
 9. Thevoltage and current sensor as in claim 7, wherein said voltage sensorboard includes, in order radially outward, said capacitive plate, aninsulator layer, a ground plate completion conductive layer, and acircuit board carrying voltage pickup components, with at least oneelectrical conductor passing from said capacitive plate through openingsin said insulator layer and said ground plate completion conductivelayer to said voltage pickup components.
 10. The voltage and currentsensor as in claim 9 wherein said voltage pickup components aresymmetrically distributed upon said board so as to create an electricalsymmetry in both axial and transverse directions.
 11. The voltage andcurrent sensor as in claim 7, wherein said current sensor boardincludes, in order radially outward, said inductive pickup conductor, aninsulator layer, a ground plate completion conductive layer, and acircuit board carrying current pickup components, with at least oneelectrical conductor passing from each end of said inductive pickupconductor through openings in said insulator layer and said ground platecompletion conductive layer to said current pickup components.
 12. Thevoltage and current sensor as in claim 11, wherein said current pickupcomponents are symmetrically distributed on said board so as to createan electrical symmetry both in axial and transverse directions.